First of all, let me start of by telling you how much I appreciate your response. It means a lot to me. Sorry about the lateness in my reply. Between the holidays and spending countless hours working on the Jeep I haven't been able to get back to you.
Now here is where I am at right now in relation to the Jeep. I feel like it is getting closer and closer to being fixed.
I have done all of the things you mentioned except for scanning for codes, and still it would do the cutting out. However, after cleaning the Idle Air Control Valve / Throttle Body on both sides. The Jeep has never really sounded any better. So that was much needed even though it is still shutting off. I also replaced the Crankshaft Position Sensor in which I heard was a prevalent problem in Jeep XJs. I also grabbed an Engine Coolant Temperature Sensor as well.
The last two days I have let the vehicle idle. Both times it went dead after idling for 1 hour and 10 minutes. So both times it did idle for more than an hour before making that sound heard in the Youtube link I posted in my previous post. When the vehicle shuts down you always have to give it at least 30 minutes before it will fire back up.
I was pleased with the progress in terms of the vehicle sounding better than it has in a long long time and really even better than any time since I have had it. I was getting a bit frustrated because I am running out of things that can be wrong with the vehicle.
I began to fiddle around with the vehicle some more, and my arm moved the ignition coil wire ever so slightly and it killed the engine in the manner shown in the Youtube Video I posted in the last post that I posted. That ignition coil was on there for over an hour, and right at the 1 hour and 10 minute mark.
So I went and got the old ignition coil wire that I originally had on the Jeep before I bought that other ignition coil wire. Instead of the vehicle having to wait 30 minutes to fire up like it normally does. It fired up again as soon as I put that Ignition Coil wire on that hadn't been on. It only stayed on for 15 minutes or so before stalling out, but in that 15 minutes it ran like a top.
So some how that ignition coil wire is getting hot and when you put a cold one that hasn't been run back on it. It fires right back up without having to wait 30 minutes. So I am wondering if I am looking at an Ignition Coil Wire issue, Ignition Coil Issue, or Distributor Cap issue. I have already replaced all 3 but since I hate some brands at big box automotive retailers in which I won't name names. I went to the junk yard to get all three of those replacement parts because they are Mopar brand and there isn't any places here who carry Mopar branded parts. The cap wasn't cracked or anything, and the Ignition Coil looked good as well, but I know that there can always be something wrong with them internally that a visual inspection will not capture.
Also: I don't know if this will help any, but it seems like the cooler it is outside. The longer it will run. For example if it is 65-70 Degrees like it was the other day it only idled for 35 Minutes before going dead. The last couple of days it has idled it has been roughly 50 degrees and it has idled longer at an hour and 10 minutes before shutting off. The only things that have been changed between the 35 minute and 1 hour and 10 minute idling times has been the Crankshaft Position Sensor and Engine Coolant Temperature Sensor.
I would really love your input on what you think might be the issue with the coil wire acting like it is. It would be greatly appreciated and I thank you for your time that you have spent so far with me.
Sunday, January 3rd, 2016 AT 8:13 AM